They don't - why do you think they do?
Constellations appear to move in the sky due to the Earth's rotation on its axis. As the Earth rotates, different constellations become visible at different times of the night. This motion is also why constellations appear to shift positions throughout the year.
The constellations appear to move across the sky due to the Earth's rotation on its axis. As the Earth spins from west to east, different parts of the sky come into view throughout the night. Additionally, as the Earth orbits the Sun, the position of constellations changes over the course of the year, leading to different constellations being visible in different seasons.
...rotation.
since earth rotates, the constellations will seem to move across the sky.
They seem to move to the West, like the Sun does.
No - as Earth rotates the stars and constellations seem to move. Also, as Earth orbits the sun over the course of a year, the stars we see at night in the winter are different than the stars we see at night in the summer. Same with Spring and Fall.
Earth orbiting the sun
The sun doesn't actually move the earth moves so does the constellations and the stars. We see them move because the solar system spins on an axis just like earth but the earth moves much faster. So we see things move but at a very slow pace all day. The constellations and stars in the sky seem to move because just like all planets they move with the solar system.
That's the Earth's rotation.
Regulus appears to move across the sky due to the rotation of the Earth on its axis. As the Earth spins, different stars and constellations become visible while others seem to set below the horizon. This apparent movement is known as diurnal motion.
The constellations are simply stars out in space - as Earth rotates, everything appears to move across the sky. Earth also moves around the Sun throughout the year, so the stars that are behind the sun in the summer, are the ones we see at night in winter.
Constellations are human interpretation to how stars seem to make shapes and patterns. Most constellations need a lot of imagination to be seen and different cultures have interpreted them differently. The constellations are also not really there in the sense that what we see as flat images in the sky are actually three dimensional with stars hundreds of light years apart.